Spin-density-wave antiferromagnetism in chromium alloys

Abstract

The account given here of the macroscopic and microscopic physical properties of antiferromagnetic (AFM) chromium alloys supplements the previous review of spin-density-wave (SDW) antiferromagnetism in pure Cr. The existence of an incommensurate spin-density wave results from Fermi-surface nesting, which changes with electron concentration as atoms of different valence are introduced into Cr. This gives rise for most impurities to a prototypical composition-temperature ($x\ensuremath{-}T$) magnetic phase diagram, which is described quite well by a model of nesting electron-hole octahedra and electron reservoir, with changes in the amplitude of the spin-density wave and its wave vector corresponding to the changes with impurity concentration of the N\'eel temperature. There are, however, numerous cases of idiosyncratic behavior in the $x\ensuremath{-}T$ phase diagram, some of which appear to correspond to unusual features in the pressure-temperature ($p\ensuremath{-}T$) phase diagram, e.g., in the CrFe, CrAl, and CrSi alloy systems. With these exceptions and a few others, the effect of impurities in the same group of the periodic table is fairly similar, so that this classification is used for the description of both the $x\ensuremath{-}T$ and $p\ensuremath{-}T$ phase diagrams. The properties of the alloy systems for each group of impurities are first summarized in the context of the $x\ensuremath{-}T$ phase diagram. The general features of the various physical properties are then considered: (1) magnetic susceptibility, whose temperature dependence signals the existence of local moments in some cases; (2) transport properties, in particular, electrical resistivity and thermopower, which show characteristic temperature dependence corresponding to the occurrence of spin fluctuations around the N\'eel temperature ${T}_{N}$, and in some cases well into the paramagnetic phase, followed below ${T}_{N}$ by effects due to the electron-hole condensation in the ordered AFM phase, and in some cases at lower temperatures to the formation of local impurity states; and (3) magnetoelastic properties, which show large effects associated with the spin-density wave and with SDW fluctuations in Cr alloys just as in pure Cr. Analysis of magnetic anomalies in the thermal expansion and bulk modulus in terms of magnetic Gr\"uneisen parameters is employed for some Cr alloy systems to describe the large body of experimental data. The empirical correspondence between increasing volume and increasing electron concentration is illustrated for several systems. The study of dilute Cr alloys provides insight into the reason for pure Cr having a weak first-order N\'eel transition, and provides examples of other phase transitions, including the incommensurate-commensurate SDW, the spin-glass, and AFM-superconducting phase transitions. The similarities between the incommensurate SDW fluctuations in Cr and Cr alloys and in the high-temperature superconducting cuprates strongly motivates, in particular, the examination of the inelastic neutron-scattering results. Optical properties provide an interesting picture of the relation between the magnitude of the energy gap at the Fermi surface and the N\'eel temperature, which is quite different in the incommensurate and commensurate SDW alloys. Local probes providing microscopic information about the environment of an impurity are clearly of great potential value in Cr alloy systems. The M\"ossbauer effect has, however, yielded disappointingly little information, but other probes such as perturbed angular correlation and nuclear magnetic resonance have provided interesting results.